Question

Find the equation of the line perpendicular to y=-2/3x -7 that runs through the points (6,1) in slope intercept form

Answer 1

The equation of line is:

$y = \frac{3}{2}x-8$

Further explanation:

Given equation of line

$y=-\frac{2}{3}x-7$

Comparing it with the standard form

y = mx + b gives us:

slope = m1 = -2/3

Let m2 be the slope of second line

The product of slopes of two perpendicular lines is -1.

$m_1* m_2 = -1\\-\frac{2}{3} *m_2 = -1\\m_2 = -1 * -\frac{3}{2}\\m_2 = \frac{3}{2}\\Putting\ in\ standard\ form\\y = \frac{3}{2}x +b$

We have to find the value of b. So, Putting the point(6,1)

$1 = \frac{3}{2}(6) +b\\1 = (3 * 3) + b\\1=9+b\\1-9 =b\\b = -8\\The\ final\ equation\ is:\\y= \frac{3}{2}x -8$

Keywords: Coordinate geometry, Point-slope form

Learn more about coordinate geometry at:

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